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First let me point you to this thread where all of these issues have been discussed already.

But as for your options:

A and C are highly unlikely.

Why would Mexico be part of the same government as the US and Canada? If Spanish wizards never arrived in the New World, then they would probably have Aztecs and various other people running whatever governments are in existence.

If the magical US managed to maintain the same borders as the Muggle US, then they would have had to exactly duplicate the wars against Mexico, to gain the exact amount of territory as the Muggle US, including the Gadsen Purchase. I see no reason that wizards would ever buy the same land as the Muggles.

This isn't even addressing Hawai'i and Alaska or the various cessions that the Muggle US has gotten through treaties with Britain.

B is the most plausible though there's no reasons that these borders have to have any rhyme or reason when compared to Muggle borders or Muggle history... e.g. Polish Florida!

Government:

I'm not sure where you're going with this term oligarchy. People can claim that the modern Muggle US is an oligarchy because to get anything actually done you have to be fabulously wealthy.

It is never, at least to my knowledge, discussed how exactly the Minister of Magic in Great Britain is chosen. They might not have a democracy either, at least not in the sense of a popular vote. Check here and here for more information on that side of it.

The shape of a particular government is intimately related to the history of an area. What do you think wizarding American history is like? Were there British settlers or did the American Indians fight them off? Was there a treaty signed? Did the British obey the treaty? Were there French or Spanish or anyone else trying to settle there? Would Spain or Mexico have retained greater lands in the western part of the US?

Why were the British wizards leaving Britain?

Early British settlers in the US try to get rich (gold, cotton, tobacco, etc) or were searching for their religious freedom (Pilgrims).

By the time the Founding Fathers roll around, they've absorbed a lot of Enlightenment talk about democracy and power for the people.

This doesn't mean wizards would have done the same.

Would all of these areas have different histories that would make them less inclined to work together? e.g. multiple countries Or would they try to work together in some form of federation of states? e.g. more like the structure of the Soviet Union.

I highly doubt that a strong federal system like the government of the modern US is what wizards would have.

How would the border lines and regions be affected for wizards and witches in the US? Would they:

A) All be under one country, consisting of Canada, the continental US, and possibly Mexico or Alaska?

B) Would they be separated into different regions such as the Northwest Territories, New England Territories, Old South, etc.

Or

C) Personally, I think its highly unlikely, but could it be the same as our Muggle borders?

So that leads me to wonder how their government would work. I think it would most likely be some sort of democracy or oligarchy?

Input please?

Rowling seems to take it for granted that the borders are exactly the same: in Quidditch Through the Ages, she mentions several teams from both the USA and Canada. She also talks about teams from Uganda and Tanzania, countries which probably wouldn't exist in the wizarding world since they are products of European colonialism. I don't think J.K. Rowling really considered the possibility that wizarding political geography would be very different, so if you want to stick strictly to what is implied in canon, there would be no change in borders in North America.

I find this unlikely, so I prefer to take a blind eye to canon when it comes to geography. It is almost certain that wizards would make their own countries in the New World. Since you are completely free to make up the history of wizarding immigration and settlement, there is quite literally nothing preventing you from making up whatever you want. If you want a sort of federation of wizarding territories, go ahead. A jumble of warring republics - why not? You can have complete anarchy, or a megalomaniacal empire span the continent. As long as you provide a good enough back story, I think you can just about justify anything you want.